Effect of the dynamic contact angle on electromagnetically driven flows in free liquid films

We study the effect of a dynamic contact angle on an electromagnetically driven flow in a horizontal free electrolyte film stretched between two coaxial cylindrical electrodes and placed in a uniform magnetic field. The flow dynamics and film deformation are described using the reduced hydrodynamic model derived in the lubrication approximation in [A. Pototsky and S. A. Suslov, J. Fluid Mech., 984, A75 (2024)]. The linearized molecular kinetic model is used to relate the dynamic and static contact angles to the wetting-line friction coefficient. Steady azimuthal flow is found for arbitrary static contact angles. Linear stability of the base azimuthal flow with respect to azimuthally invariant perturbations is studied using the numerical continuation method. We find that the flow stability is highly sensitive to variations of the wetting-line friction coefficient and the static contact angle. The least stable azimuthal flow is found for the frictionless contact line corresponding to a free film that remains perpendicular to the surface of the electrodes. The azimuthal flows are found to experience a supercritical Hopf bifurcation upon which they transition to a stable oscillatory dynamic regime characterized by alternating squeezing and swelling of the film near the inner and outer electrodes.